The Improved Research On Trust Region Algorithms Of Non-smooth Optimization

Optimization method is a very strong discipline of applicability, it is an important component of operations research, optimization method can solve a lot of practical problems. Non-smooth optimization is an important branch of optimization. Therefore, studying on such a research is of great significance.For unconstrained non-smooth optimization problem, how to design a fast and effective algorithm has been much attention, in which trust region algorithm for solving unconstrained non-smooth optimization problems is a kind of effective method. In recent years, the research on trust region algorithm is more perfect, but for non-monotone trust region algorithm theory research is still not perfect.In this paper,first the background and present situation of discussed problem are narrated, then some preliminaries are introduced. On this base, non-smooth trust region algorithms are presented in detail. Most of the importance, the improved trust region algorithms and Non-monotone trust region algorithms for Non-smooth optimization are suggested. The Non-monotone algorithms relax the condition of accepting attempt step, and in some degree, the"Marotos"effect can be overcomed,which is generated in constrained optimization.Not only did the combination of trust region strategy and non-monotone line search technology keep the character of trust region algorithms, but also relax the condition of accepting attempt step, which make new algorithm efficient. In theory, the convergence of the algorithm is proved . The validity of the algorithm is also suggested by numerical experiment.